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Postgraduate research

The Department of Mathematics runs an active PhD research programme covering an array of topics. Currently, our PhD researchers are working on topics such as discrete mathematics, algebra, cryptography, number theory, quantum chaos and quantum information. All of our academic staff are happy to take on new PhD students but some may temporarily stop accepting new students if they become overloaded.

You can find out about our current PhD students and their research fields in our directory.

We welcome applications from prospective PhD students wishing to propose their own research projects, or those who wish to develop a detailed project in conjunction with their supervisor. We also welcome those of you who wish to work on projects of particular interest to our academics. A list of such projects and suggested research topics can be seen here. The latter are encouraged to contact the listed supervisor directly, either before or in parallel, with making a formal application.

Prospective Postgraduate research students

The PhD programme at the Department of Mathematics is research-based and much of the work involves substantial amounts of research and study, both independently and in close coordination with your supervisor. All of our PhD research students are assigned at least one named supervisor and an advisor, both of whom are academics from our department. Your supervisor directs your work and acts as your first line of research and welfare support while the role of your advisor will vary but in all cases they provide a second line of support.

You may also be directed to attend some of the advanced course units offered by the College. To make the most of your PhD programme, it’s important you play an active role in the department’s research community. This involves regularly attending relevant seminar series, workshops and study groups in the department. It also involves discussing and presenting work to your fellow students and staff. Where appropriate, you may even have the chance to attend or present your work at seminars, workshops or research meetings off campus, including international research conferences.

Once your research has been successfully completed, you must write and submit a final report in the form of a PhD research thesis. This will be evaluated by at least two experts and you’ll be invited to attend an oral examination, known as a Viva, where you must defend your thesis.

How long will my PhD take?

The most common and practical mode of pursuing a PhD is to study full-time. Full-time students in their first three years are guaranteed desk space and computer facilities in the department and are expected to fully contribute to our research community. You have four years from your registration to submit your thesis.

We also welcome applications for part-time study from committed candidates. This is the default mode for students working for more than 15 hours per week or with family commitments that may prevent full-time study. If you’re a part-time student you’re expected to attend Royal Holloway’s campus on a fairly regular basis. You’ll have seven years from your registration to submit your thesis.

Before registering for a PhD degree, you must ensure that time and funds will be available to enable your completion and submission of your thesis within four or seven years.

You can find more detailed information about what is available in the Departmental Research Postgraduate Handbook.

The minimum entry requirement for an MPhil or an MPhil leading to a PhD degree is the equivalent of a UK Second Class Honours degree in an appropriate subject. In many cases, a Master’s level qualification is also expected.

Candidates must also be demonstrably proficient in spoken and written English. Find out more here.

Prospective postgrad research students

You can find out the current fees for postgraduate study at Royal Holloway as well as more information about payment plans and how to pay your fees on our tuition fee pages.

When trying to work out how much money you’ll need please consider:


  • Fees are charged at different rates for citizens of the European Union and overseas students who are not from the European Union.
  • Full fees are due for the first three years of a full-time PhD research programme. Students requiring a fourth and final year to write up their thesis pay a much reduced ‘writing-up’ fee.
  • Part-time fees are half the full-time ones. Students requiring a seventh and final year to write their thesis pay a much reduced fee.
  • You cannot submit your thesis before the end of your second year of full-time study (fourth year of part-time study).

You must make sure you have sufficient funds (both to cover fees and living costs) to complete a PhD study programme, especially now that there is a four year limit for full-time study (seven year limit for part-time study). 

Obtaining funding can be extremely difficult so potential candidates are advised to actively explore all available opportunities to secure funds. There are generally two classes of funding that PhD students use to support their studies, with many combining their sources of funds.

External funding

External funding describes funds that students obtain themselves and have nothing to do with Royal Holloway. Common sources include:


  • Scholarships – these most commonly come from national governments but some industrial organisations offer PhD research scholarships.
  • Employers – Some employers offer support for employees to complete PhDs.
  • Private funds – Some students rely on private funds to support their studies.

Internal Funding

These are mostly dedicated funds allocated to the department, which we can use to support PhD research students.

Please note that internal department funding is:


  • Extremely limited – We can only support a very small fraction of the PhD applicants we make offers to in a typical year.
  • Often partial – Many of the awards we allocate only cover home fees or part of an overseas fee.
  • Not necessarily applied for – We automatically consider all PhD applicants to whom we have made an offer when we allocate internal departmental funding. It is therefore important to apply to our PhD programme even if you have not secured funding yet as it means we can consider you for all our internal awards.

Examples of Internal Funding include:


  • Royal Holloway Studentships – Every year the department is allocated a small number of partial scholarships, which typically only pay for home fees or part of an overseas fee. Occasionally awards also cover maintenance. These awards cannot be directly applied for. Allocations of these awards are made to selected applicants before June of each year for students beginning their course the following September.
  • Project Studentships – These are normally full awards obtained when a particular academic receives a research grant that includes support for a PhD studentship. These include EPSRC CASE awards where the project involves collaboration with a company. Project Studentships tend to be advertised on our website although qualified candidates with current PhD offers are likely to be considered or encouraged to apply.
  • Assistantships – These are typically partial awards and involve specified part-time duties in the department. Recent assistantships have involved supporting undergraduate teaching and the MSc programmes. Assistantships are usually advertised although qualified candidates with current PhD offers are likely to be considered or encouraged to apply.

Please check Royal Holloway’s funding page for more information.

You can either apply by downloading an application form or applying online. Find out more here.

Please do not apply directly to the department.

Whether you apply in writing or online, the following four pieces of information should ideally be included in your application (these can be covered in sections labelled Research Proposal, Supporting Statement or in a combined attachment).


  1. An explanation as to why you wish to pursue PhD research in mathematics
  2. A personal statement that explains why you think you would fit into our research group
  3. An indication of the research areas that most interest you (you don’t have to formally define a full research project but you’re welcome to do so)
  4. An indication of which staff you think might make potential supervisors. It is useful, but not essential, to have contacted potential staff in advance.

The main goal of this section is to assist us in processing your application, by learning your research interests, background, experience and career goals we can identify potential supervisors.

Once we receive your application, we will circulate it among potential supervisors. We will contact you as soon as a decision is made. In certain circumstances we may wish to contact you to request further information or invite you to visit the department.

Please note that an offer is dependent on a supervisor being available to support your PhD research study. Occasionally qualified candidates may be turned down simply because we don’t have available supervision.

If you want further information or wish to discuss your application please contact Professor Pat O'Mahony.


Postgraduate overview

Film courtesy of PostgraduateSearch.com


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